In an ion beam-plasma system, low frequency self-oscillations are observed when an ion beam with a velocity near the ion acoustic velocity is injected into the plasma. This oscillation has a discrete spectral structure which results from the fact that the system is axially bounded. A real wave number for each discrete excited mode is determined by the bounded length. The self-oscillation frequency is approximately proportional to the wave number and to the ion beam velocity. These properties of the oscillation are quantitatively explained by the kinetic dispersion relation for the two stream ion-ion instability in the ion beam-plasma system.